Definition
Regrouping
Regrouping rewrites the same quantity with different place-value groups so a calculation is easier or possible.
What it means
A number can be packed in more than one way. One ten has the same value as ten ones, so 34 can be shown as 3 tens and 4 ones or as 2 tens and 14 ones. Regrouping makes that exact trade while keeping the total unchanged.
Remember it
Trade the groups, not the amount: 1 ten ↔ 10 ones.
Example
To calculate 43 − 27, 3 ones are not enough to subtract 7 ones. Exchange 1 of the 4 tens for 10 ones, so 43 becomes 3 tens and 13 ones. Subtract 2 tens and 7 ones to get 1 ten and 6 ones, which is 16.
Watch for
Changing 34 into 2 tens and 13 ones is not correct regrouping, because that representation is worth 33 rather than 34.
Common mix-up
“Borrowing” sounds as if a ten will be returned. Regrouping is an exact exchange: one ten becomes ten ones, so the value stays the same.
Exact meaning
Regrouping changes how a quantity is represented without changing its value. In base ten, one unit in a place is exchanged for ten units in the place immediately to its right, or ten units are exchanged for one unit in the place immediately to its left.